Question

$\huge \bold \red{\boxed{ \bold{ \int \frac{ {e}^{x} }{x} \: dx}}}$​

Answer 1

$\displaystyle{ \bold \red{\int{\frac{e^{x}}{x} d x}}}$

This integral (Exponential Integral) does not have a closed form:

${ \displaystyle{ \bold \color{red}{\int{\frac{e^{x}}{x} d x}} = \color{red}{\operatorname{Ei}{\left(x \right)}}}}$

Therefore,

$\displaystyle \bold \red{\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}}$

${ \displaystyle{\bold \red{ \int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}+C}}}$

Answer 2

Answer:

$\displaystyle{ \bold \red{\int{\frac{e^{x}}{x} d x}}}$

This integral (Exponential Integral) does not have a closed form:

${ \displaystyle{ \bold \color{red}{\int{\frac{e^{x}}{x} d x}} = \color{red}{\operatorname{Ei}{\left(x \right)}}}}$

Therefore,

$\displaystyle \bold \red{\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}}$

${ \displaystyle{\bold \red{ \int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}+C}}}$